Magnetic resonance imaging (MRI) is established as a medical imaging modality. MRI provides a number of significant advantages but also entails various restrictions. One of these restrictions is that in many cases magnetic resonance capture procedures take a relatively long time, with the possibilities of accelerated image acquisition being severely limited. If it is crucial to achieve good temporal resolution, the temporal scanning rates of magnetic resonance imaging are often limited and include specific disadvantages and/or require very complex procedures.
The temporal scanning rate of magnetic resonance imaging is primarily a function of the magnetic resonance sequence used, where specific gradient echo (GRE) magnetic resonance sequences are predominantly used.
Initially in relation to target imaging modalities, the concept of compressed sensing may be used. Compressed sensing is a reconstruction technique that may be applied to measurement data of an imaging modality that has been subject to temporal and/or spatial subsampling. Compressed sensing is based on the observation that not only natural images—e.g. photographs—may be subjected to compression with little or no visible loss of information, but also that medical images may also be subject. If the images that are to be captured are compressible, most transform coefficients may be left out of account or are insignificant. As such, it is not necessary to capture all the measurement data. The mathematical theory for compressed sensing provides the possibility of reconstructing, from subsampled measurement data, image data sets that are still largely free of artifacts even if the Nyquist criterion is not fulfilled.
With compressed sensing, instead of the direct reconstruction of the image data set, a sparse version of the image data set may be reconstructed, in which substantially fewer image elements contain significant image values. The mathematical principle of compressed sensing is that the candidate data set for the image data set in which the l1 norm is at a minimum will be the correctly reconstructed data set of the candidate data sets for the data that results when a measurement operator that maps measurement of the measurement data is applied to the candidate data set. Using an optimization method, for example a minimization method, the candidate data set for which the target function containing the l1 norm of the sparse version of the candidate data set is at a minimum may be identified, given the boundary condition that the measurement data results again from the image data set under the measuring conditions.
In order to generate sparse versions of the candidate data set, various transforms, called “sparsifying operators” are used. If, for example, a gradient operator is applied to a candidate data set, the only remaining significant pixels are the edges visible in the candidate data set. The result is markedly sparser than the original candidate data set. Other frequently used examples of sparsifying operators are wavelet transforms. The application of a sparsifying operator corresponds substantially to mapping the image values of the candidate data set onto a sparse vector of coefficients that are associated with the corresponding basis functions of the sparsifying operator.
A paper by Michael Lustig et al., “Sparse MRI: the Application of Compressed Sensing for Rapid MR Imaging”, Magnetic Resonance in Medicine 58:1182-1195 (2007), describes the application of compressed sensing to accelerated magnetic resonance imaging. There, the sparsity that is implicit in MR images is exploited, where implicit sparsity is meant as transform sparsity, i.e. the underlying object in the magnetic resonance imaging that is to be imaged in the image data set has a sparse representation in a known and fixed mathematical transform domain. Here, “sparsity” referred to that there are relatively few significant pixels with nonzero values, that may also equally well be meant in a temporal dimension. However, the degree of possible subsampling in magnetic resonance is still limited, for example if a certain spatial resolution is to be maintained, since shortening the capture time or the temporal scanning rate of magnetic resonance imaging continues to result in a deterioration in the spatial resolution. Even if compressed sensing is used, the possibility of accelerating magnetic resonance imaging is thus limited.
Compressed sensing has also already been proposed for other medical imaging modalities, such as computer tomography, for example in an article by Guang-Hong Chen et al., “Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets”, Medical Physics 35: 660-663 (2008). The article refers to dynamic CT imaging in which streaking artifacts occur if the Shannon/Nyquist requirements are not satisfied. Accordingly, the compressed sensing approach is extended in that the temporal change in the CT measurement data is not taken into account and a prior image is generated as an additional boundary condition. There are also constraints in computer tomography and other medical imaging modalities as to the degree to which subsampling is possible while allowing compressed sensing.